- Email: [email protected]
Magnetic moment of the 405 keV (72 −) level in 211Bi
Volume 19, number 7
PHYSICS LETTERS
v a l u e s f o r t h e s e s t a t e s i s 0.77 MeV which i s a l m o s t e x a c U y that for the g r o u n d and f i r s t e x c i t e d s t a t e s of 31Si (0.76 MeV). The r e l a t i v e l y l a r g e i n t e n s i t i e s of t h e s e s t a t e s (the 7.15 and 6.38 MeV s t a t e s have i n t e n s i t i e s equal to 90% and 76% of the 3 1 p g r o u n d s t a t e and f i r s t e x c i t e d s t a t e intens i t i e s , r e s p e c t i v e l y ) , coupled with the r e s u l t s given above m a k e it r e a s o n a b l e to identify the 6.38 MeV s t a t e a s the f i r s t T = } s t a t e of 31p c o r r e s p o n d i n g to the g r o u n d s t a t e of 31Si and the 7.15 MeV s t a t e a s the s e c o n d T = l2 s t a t e of 3 1 p c o r r e s p o n d i n g to the f i r s t e x c i t e d s t a t e of 31Si. F r o m the above c o n s i d e r a t i o n s the s p i n and+parity of the 6.38 MeV s t a t e can be r e s t r i c t e d to ~ . A c o m p a r i s o n of t h e s e and other r e s u l t s obt a i n e d d u r i n g the p r e s e n t e x p e r i m e n t with the p r e d i c t i o n s of n u c l e a r m o d e l s will be p u b l i s h e d later.
15 December 1965
t h i s work. One of the a u t h o r s (W. G. D.) would like to thank the National R e s e a r c h Council for financial assistance.
References
1. W.G.Davies, W.K.Dawson, G.C.Neflson and K. Ramavataram, Nuclear Phys., in press. 2. B.Cujec, W.G.Davies, W.K.Dawson, T.B.Grandy, G. C. Neflson and K. Ramavataram, Physics Letters 15 (1965) 266. 3. L . L . Lee and J. P. Sohiffcr, Phys. Rev. 136 (1964) B405. 4. W.G.Davie~, W.K.Dawson and G.C.Neilson, to be published. 5. G . I . H a r r i s , H.J.Hennecke and F.W. P r o s s e r , Physics Letters 9 (1964) 324. 6. G.I. Harris and L. W. Seagondollar, Phys. Rev. 131 (1963) 787. 7. H.A.Van Rinsvelt and P. M. Endt, Physics Letters 9 (1964) 266. 8. P.M.Endt and C.Van der Leun, Nuclear Phys.34 (1962) 1.
The a u t h o r s would like to acknowledge the help of Dr. K. R a m a v a t a r a m d u r i n g the c o u r s e of *****
MAGNETIC
MOMENT
OF
THE
405
keV
(½-)
LEVEL
I N 2 ~i 1lB
Y. K. AGARWAL, C . V . K . BABA *, S . K . B H A T T A C H E R J E E and D. C. E P H R A I M Tata Institute of Fundamental Research, Bombay, India
Received 9 November 1965
The m a g n e t i c m o m e n t s of the g r o u n d s t a t e s and the l o w - l y i n g e x c i t e d s t a t e s of the o d d - A nuc l e i n e a r the d o u b l y - c l o s e d 208pb n u c l e u s have r e c e n t l y r e c e i v e d i m p o r t a n c e f r o m the point of v i e w of c o r e p o l a r i z a t i o n e f f e c t s [1-3]. The m a g n e t i c m o m e n t s of the g r o u n d s t a t e of 209Bi (h~) and the px g r o u n d s t a t e and f~_ e x c i t e d s t a t e of 2071~b ~aave b e e n m e a s u r e ~ and a n a l y s e d in d e t a i l [3, 4]. In t h i s context, it would be v e r y int e r e s t i n g if the m a g n e t i c m o m e n t of the 910 keV (fI) s t a t e [5] in 20gBi could be m e a s u r e d . But unfo~'tunately t h i s s t a t e i s not a m e n a b l e to m e a s u r e m e n t s with p e r t u r b e d a n g u l a r c o r r e l a t i o n m e t h o d s . H o w e v e r , the 405 keV (½-) s t a t e in 211Bi has b e e n i n t e r p r e t e d [6] a s the f1 s t a t e in r e c e n t s t u d i e s on the b e t a - d e c a y of 36 mien 211pb [6-8]. The p r e s e n t note d e s c r i b e s a m e a s u r e m e n t of the m a g n e t i c m o m e n t of t h i s s t a t e in 211Bi. A p a r t i a l d e c a y s c h e m e of 36 min 211pb [6-8] * Member, Atomic Energy Establishment, Trombay. 578
is shown in fig. 1. The h a l f - l i f e of the 405 keV l e v e l h a s b e e n m e a s u r e d a s 315 ± 20 p s [6]. The m e a s u r e m e n t s w e r e m a d e on the 702 - 405 keV c a s c a d e in 211Bi f o r which the d i r e c t i o n a l c o r r e lation c o e f f i c i e n t s have b e e n m e a s u r e d [6, 7]. B e c a u s e of the s h o r t h a l f - l i f e of 211pb~ m o s t of the m e a s u r e m e n t s w e r e m a d e with a 211pb s o u r c e in e q u i l i b r i u m with 223Ra (t~ = l l . 6 d) which was s e p a r a t e d f r o m 22 y 227~c by r a d i o c h e m i c a l m e t h o d s . The g a m m a r a y s in the decay chain [9] of 223Ra-~ 211pb do not c a u s e any int e r f e r e n c e in the m e a s u r e m e n t of the d i r e c t i o n a l c o r r e l a t i o n of the 7 0 2 - 405 keV c a s c a d e . Some m e a s u r e m e n t s w e r e a l s o c a r r i e d out with 211pb s o u r c e s , s e p a r a t e d f r o m 223Ra i o n - e x c h a n g e technique [6]; 211pb s o u r c e s w e r e m i l k e d e v e r y two h o u r s f r o m the i o n - e x c h a n g e column. About 100 s u c h s o u r c e s w e r e u s e d in the c o u r s e of this work. The e x p e r i m e n t a l a r r a n g e m e n t for m e a s u r i n g the m a g n e t i c m o m e n t has been d e s c r i b e d e a r -
Volume 19, number 7
PHYSICS LETTERS E
I rr
211
+ Pb 9/2 -
-
( 56 min)
(KeV)
~
a2ss
~
.......
8
427
702
1''~(7"4) ],,~)(2~) ,o.5~) 4~ I
766
t~2= 0"315 n| 5
o 9/; 83
Bi
211
(2"2rain)
Fig. 1. Partial decay scheme of 36 min 211pb from refs. 6-8. Only the intense ~ and y transitions together with their intensities are indicated. The numbers given in parentheses refer to the log f l values of the /3 transitions. l i e r [10]. The directional correlation coefficients of the 702-405 keV cascade have been measured both with 211pb and 223Ra sources. The measurements were made in the actual geometry used for the magnetic moment determination. The data were analysed only for A 2 since the value of A 4 was found to be negligible [8, 7]. The directional correlation coefficient, A2, corrected for geometry, is in excellent agreement with e a r l i e r measurements [6, 7]. The magnetic moment measurements were made by an integral method using an external magnetic f i e l d of 18.3 kG applied perpendicular to the plane of the two gamma rays. The chance coincidence rate for any source was never more than 15~ of the total coincidence rate. The experimental a s y m m e t r y R(135 °) defined by
R(135o) = 2 W(135o, +H) - W(135o, -H) W(135 °, +H) + W(135 °, - H ) was measured with beth kinds of sources and the results are summarized in table 1, The measured a s y m m e t r y R is related to the L a r m o r precession frequency by
o~(=gl~NH/h~
R(135 °) = 3A2w~/(1 + 0.25A2)
,
where r i s the m e a n Hie of the 405 keV state. The m e a s u r e m e n t s with both kinds of s o u r c e s a g r e e d with each other, and the weighted a v e r a g e s of A 2
15 December 1965
Table 1 S,rmr~ary of the results. The directional correlation measurements on the 702 -405 keV cascade were analyzed only for ,42. The values of A 2 given in the table are not corrected for geometry. Source
.42
R(in %)
211pb 223Ra
-0.092 ± 0.007 -0.087 * 0.007
-1.39 :L0.40 -1.39 ± 0.21
Average
-0.090 ±0.005
-1.39 +0.19
g
1.27 -0.20
and R lead to a value of g = 1.27 * 0.20 c o r r e sponding to /~ = 4.45 ~- 0.70 n.m. We u s e d liquid s o u r c e s for the m e a s u r e m e n t s and no e x t r a nuc l e a r p e r t u r b a t i o n s on A2 w e r e a s s u m e d . The Schmtdt value for the m a g n e t i c m o m e n t of an f~ p r o t o n i s 5.79 n . m . The m e a s u r e d value of /~ i s ' s u b s t a n t i a l l y lower, c o r r e s p o n d i n g to an effective spin g - f a c t o r g s eft = (0.52 ± 0.25)g s free" A s s u m i n g the 405 keV sta'te to be a pure f ! st~'te, 2 one could e s t i m a t e the effect of core p o l a r i z a t i o n in a m a n n e r s i m i l a r to that of the f i n e u t r o n - h o l e state in 207pb [4]. In this model, t~e m a g n e t i c m o m e n t o p e r a t o r i s modified to [2] t, op -- ~s.p. ÷ 8 g s S + g p ( - r 2 a h • The v a l u e s of 5g s and gD for the 208pb core have b e e n obtained [4] f r o m the m e a s u r e d m a g n e t i c m o m e n t s of the ground s t a t e s of 207pb and 209Bi as 5g s = 5.21 a n d g n = 3.10. A s s u m i n g tlmt the s a m e p a r a m e t e r s c~h~.racterize the 21Opb core also, one can c a l c u l a t e the m a g n e t i c m o m e n t of the f~ s t a t e in 21113i a s ~ = 3.59 n . m . which i s in f a i r a g r e e m e n t with the m e a s u r e d value of ~ = 4.45 ± 0.70 n.m. It would also be i n t e r e s t i n g to make a d e t a i l e d c a l c u l a t i o n on the l i n e s of ref. 3 for this case also. The f i r s t excited 2+ state i n 210pb i s at 780 keV. Hence one m a y also i n t e r p r e t the 405 keV state in 211Bi as a {(g~2)2+ , h i } l - state. In fact, the z e r o o r d e r energy2of such2a2state i s expected to be 780 keV while the e x c i t a t i o n e n e r g y of a pure f~2 s t a t e i s 910 keV in 209Bi. The l o w e r i n g of the e n e r g y of s u c h a ~- state to 405 keV m a y be due to n - p i n t e r a c t i o n s . The m a g n e t i c m o m e n t of such a c o n f i g u r a t i o n can be c a l c u l a t e d if the m a g n e t i c m o m e n t s of the h~ proton and the g ! n e u t r o n a r e known. Assum~ag/z = 4.08 n . m . 2 for the h i p r o t o n (from the m e a s u r e d value of 209Bi), and the Schmidt value for the g ! n e u t r o n , the expected m a g n e t i c m o m e n t of s u c h ~ configur a t i o n is 3.9 n . m . which i s also in good a g r e e m e n t with the e x p e r i m e n t a l value. A change i n the m a g n e t i c m o m e n t of a g l n e u t r o n away f r o m the Schmidt value would n o t ' a f f e c t the expected 579
Volume 19, number 7
PHYSICS LETTERS
value of the m a g n e t i c m o m e n t of a {(g92)~+, hA)_~" 2 ~ 2 state. In this context, it will be e x t r e m e l y i n f e r e s t i n g if the m a g n e t i c m o m e n t of the ground state of 21IBi could be m e a s u r e d . A c o m p a r i s o n of the g r o u n d - s t a t e m o m e n t s of 209Bi and 211Bi would then throw light on the effect of the two g9 n e u t r o n s in p o l a r i z i n g the core. Thus it is a p p a r e n t f r o m the above d i s c u s s i o n , that the m e a s u r e d m a g n e t i c m o m e n t of 405 keV (~-) state in 211Bi i n d i c a t e s p o s s i b l e core p o l a r i zation i r r e s p e c t i v e of whether the s t a t e i s a pure f~ state or a state f o r m e d by coupling the h9 p r o ° to the ( g ~2) 2 + state of the two n e u t r o n s . ton We wish to thank Drs. C. L. Rao and M. V. R a m a n a i h for t h e i r c o o p e r a t i o n in s e p a r a t i n g 223Ra f r o m 227Ac, Dr. K. S, Bhatki for his help in m i l k i n g 211pb s o u r c e s and Mr. H. C. J a i n for his help d u r i n g the c o u r s e of the m e a s u r e m e n t s .
15 December 1965
1. A.Bohr and B.R.Mottelscm, Lectures on nuclear structure and energy levels (Institute of Theoretical Physics and NORDITA, Copenhagen) 1962. 2. E. Bodenstedt and J. D. Rogers, in Perturbed angular correlations, eds.E.Karlsson, E.Matthias and K. Siegbahn (North-Holland Publ. Co., Amsterdam,
1964). 3. J.Blomqvist, N.Freed and H.O.Zetterstrb'm, Physics Letters 18 (1965) 47. 4. S.Gustsfsson, K.Johansson, E.Karlsson and A.G. Svensson, Physics Letters 10 (1964) 191. 5. A.Z.Hrynkiewicz, St.Szymczyk, T.Walczac, G. Zapalski, F. Baldeweg and G.Stiller, Physics Letters 6 (1963) 326. 6. S.E.Vandenbosch, C.V.K.Baba, P.R.Christensen, O. B.Nielsen and H.Nordby, Nuclear Phys.41 (1963) 482. 7. C.R.Cothern and R.D.Connor, Can.J. Phys.43 (1965) 383. 8. R.O.Mead and J.E.Draper, Phys. Rev. 139 (1965) B9. 9. E.K.Hyde, I.Perlman and G.T.Seaberg, in The nuclear properties of the heavy elements, Vol. II (Prentice-Hall, Inc., N.J.) 1964. 16. Y.K.Agarwal, C.V.K.Baba and S.K.Bhattacherjee, Nuclear Phys. 58 (1964) 651.
THE
IMPORTANCE OF THE STRONG ISOTOPIC SPIN DEPENDENCE OF PARTICLE-HOLE MATRIX ELEMENTS ON T H E M A N Y P A R T I C L E - M A N Y H O L E S T A T E S IN N U C L E I * L. ZAMICK P a l m e r P h y s i c a l L a b o r a t o r y , P r i n c e t o n University, P r i n c e t o n , N e w J e r s e y
Received 10 November 1965
Following the i d e a s of B a n s a l and F r e n c h [1, 2] v e r y closely, we s h a l l t r y to d e t e r m i n e some of the p r o p e r t i e s of the excited s t a t e s of n u c l e i whose c o n f i g u r a t i o n s c o n s i s t of holes in the l p s h e l l and p a r t i c l e s in the 2 s - l d shell. We s h a l l also c o n s i d e r the f ! s h e l l b r i e f l y . If we deal with ~nly p a r t i c l e s in a given s h e l l (no holes), we can expect c o n s i d e r a b l e s u c c e s s by a s s u m i n g that the p a r t i c l e - p a r t i c l e i n t e r a c t i o n is spin independent and isotopic s p i n independent. The s u p e r m u l t i p l e t theory and E l l i o t t ' s SU(3) s c h e m e a r e e x a m p l e s of this. It has been shown, however, by Bansal and F r e n c h [1, 2], that it is a g r a v e e r r o r to a s s u m e that the p a r t i c l e - h o l e i n t e r a c t i o n is independent of isotopic spin. If one e x a m i n e s the negative p a r i t y s t a t e s of 160, which a r e e i t h e r one p a r t i c l e - o n e hole or 3 - p a r t i c l e - 3 hole excitations, one s e e s i m m e d i a t e l y * This work was supported by the U. S. Atomic Energy Commission and the Higgins Scientific Trust Fund. 580
that the T = 1 s t a t e s lie c o n s i d e r a b l y higher in e n e r g y than the c o r r e s p o n d i n g T = O s t a t e s (about 5 MeV or more). If we make the somewhat crude a s s u m p t i o n , that the s p l i t t i n g of the T = 0 and T = 1 s t a t e s (the difference of t h e i r c e n t e r s of gravity) is much l a r g e r than the splitting of different s t a t e s with the s a m e isotopic spin, then we can, as the above a u t h o r s have done, a p p r o x i m a t e the p a r ticle hole i n t e r a c t i o n by a monopole potential Hmono = - a + bt 1 t 2 ,
(1)
where - a is the c e n t e r of g r a v i t y of all p a r t i c l e hole s t a t e s with a (2J+ 1)(2T+ 1) weighting, and b is the s e p a r a t i o n of the T = 1 and T = 0 cent e r s of gravity. We expect b to be l a r g e and positive. To the above we should add the Coulomb p a r t i c l e - h o l e energy, c, which acts between a proton and a proton hole. We shall take c to equal - 0.5 MeV. We now c o n s i d e r a n u c l e u s with rn holes in the
PHYSICS LETTERS
v a l u e s f o r t h e s e s t a t e s i s 0.77 MeV which i s a l m o s t e x a c U y that for the g r o u n d and f i r s t e x c i t e d s t a t e s of 31Si (0.76 MeV). The r e l a t i v e l y l a r g e i n t e n s i t i e s of t h e s e s t a t e s (the 7.15 and 6.38 MeV s t a t e s have i n t e n s i t i e s equal to 90% and 76% of the 3 1 p g r o u n d s t a t e and f i r s t e x c i t e d s t a t e intens i t i e s , r e s p e c t i v e l y ) , coupled with the r e s u l t s given above m a k e it r e a s o n a b l e to identify the 6.38 MeV s t a t e a s the f i r s t T = } s t a t e of 31p c o r r e s p o n d i n g to the g r o u n d s t a t e of 31Si and the 7.15 MeV s t a t e a s the s e c o n d T = l2 s t a t e of 3 1 p c o r r e s p o n d i n g to the f i r s t e x c i t e d s t a t e of 31Si. F r o m the above c o n s i d e r a t i o n s the s p i n and+parity of the 6.38 MeV s t a t e can be r e s t r i c t e d to ~ . A c o m p a r i s o n of t h e s e and other r e s u l t s obt a i n e d d u r i n g the p r e s e n t e x p e r i m e n t with the p r e d i c t i o n s of n u c l e a r m o d e l s will be p u b l i s h e d later.
15 December 1965
t h i s work. One of the a u t h o r s (W. G. D.) would like to thank the National R e s e a r c h Council for financial assistance.
References
1. W.G.Davies, W.K.Dawson, G.C.Neflson and K. Ramavataram, Nuclear Phys., in press. 2. B.Cujec, W.G.Davies, W.K.Dawson, T.B.Grandy, G. C. Neflson and K. Ramavataram, Physics Letters 15 (1965) 266. 3. L . L . Lee and J. P. Sohiffcr, Phys. Rev. 136 (1964) B405. 4. W.G.Davie~, W.K.Dawson and G.C.Neilson, to be published. 5. G . I . H a r r i s , H.J.Hennecke and F.W. P r o s s e r , Physics Letters 9 (1964) 324. 6. G.I. Harris and L. W. Seagondollar, Phys. Rev. 131 (1963) 787. 7. H.A.Van Rinsvelt and P. M. Endt, Physics Letters 9 (1964) 266. 8. P.M.Endt and C.Van der Leun, Nuclear Phys.34 (1962) 1.
The a u t h o r s would like to acknowledge the help of Dr. K. R a m a v a t a r a m d u r i n g the c o u r s e of *****
MAGNETIC
MOMENT
OF
THE
405
keV
(½-)
LEVEL
I N 2 ~i 1lB
Y. K. AGARWAL, C . V . K . BABA *, S . K . B H A T T A C H E R J E E and D. C. E P H R A I M Tata Institute of Fundamental Research, Bombay, India
Received 9 November 1965
The m a g n e t i c m o m e n t s of the g r o u n d s t a t e s and the l o w - l y i n g e x c i t e d s t a t e s of the o d d - A nuc l e i n e a r the d o u b l y - c l o s e d 208pb n u c l e u s have r e c e n t l y r e c e i v e d i m p o r t a n c e f r o m the point of v i e w of c o r e p o l a r i z a t i o n e f f e c t s [1-3]. The m a g n e t i c m o m e n t s of the g r o u n d s t a t e of 209Bi (h~) and the px g r o u n d s t a t e and f~_ e x c i t e d s t a t e of 2071~b ~aave b e e n m e a s u r e ~ and a n a l y s e d in d e t a i l [3, 4]. In t h i s context, it would be v e r y int e r e s t i n g if the m a g n e t i c m o m e n t of the 910 keV (fI) s t a t e [5] in 20gBi could be m e a s u r e d . But unfo~'tunately t h i s s t a t e i s not a m e n a b l e to m e a s u r e m e n t s with p e r t u r b e d a n g u l a r c o r r e l a t i o n m e t h o d s . H o w e v e r , the 405 keV (½-) s t a t e in 211Bi has b e e n i n t e r p r e t e d [6] a s the f1 s t a t e in r e c e n t s t u d i e s on the b e t a - d e c a y of 36 mien 211pb [6-8]. The p r e s e n t note d e s c r i b e s a m e a s u r e m e n t of the m a g n e t i c m o m e n t of t h i s s t a t e in 211Bi. A p a r t i a l d e c a y s c h e m e of 36 min 211pb [6-8] * Member, Atomic Energy Establishment, Trombay. 578
is shown in fig. 1. The h a l f - l i f e of the 405 keV l e v e l h a s b e e n m e a s u r e d a s 315 ± 20 p s [6]. The m e a s u r e m e n t s w e r e m a d e on the 702 - 405 keV c a s c a d e in 211Bi f o r which the d i r e c t i o n a l c o r r e lation c o e f f i c i e n t s have b e e n m e a s u r e d [6, 7]. B e c a u s e of the s h o r t h a l f - l i f e of 211pb~ m o s t of the m e a s u r e m e n t s w e r e m a d e with a 211pb s o u r c e in e q u i l i b r i u m with 223Ra (t~ = l l . 6 d) which was s e p a r a t e d f r o m 22 y 227~c by r a d i o c h e m i c a l m e t h o d s . The g a m m a r a y s in the decay chain [9] of 223Ra-~ 211pb do not c a u s e any int e r f e r e n c e in the m e a s u r e m e n t of the d i r e c t i o n a l c o r r e l a t i o n of the 7 0 2 - 405 keV c a s c a d e . Some m e a s u r e m e n t s w e r e a l s o c a r r i e d out with 211pb s o u r c e s , s e p a r a t e d f r o m 223Ra i o n - e x c h a n g e technique [6]; 211pb s o u r c e s w e r e m i l k e d e v e r y two h o u r s f r o m the i o n - e x c h a n g e column. About 100 s u c h s o u r c e s w e r e u s e d in the c o u r s e of this work. The e x p e r i m e n t a l a r r a n g e m e n t for m e a s u r i n g the m a g n e t i c m o m e n t has been d e s c r i b e d e a r -
Volume 19, number 7
PHYSICS LETTERS E
I rr
211
+ Pb 9/2 -
-
( 56 min)
(KeV)
~
a2ss
~
.......
8
427
702
1''~(7"4) ],,~)(2~) ,o.5~) 4~ I
766
t~2= 0"315 n| 5
o 9/; 83
Bi
211
(2"2rain)
Fig. 1. Partial decay scheme of 36 min 211pb from refs. 6-8. Only the intense ~ and y transitions together with their intensities are indicated. The numbers given in parentheses refer to the log f l values of the /3 transitions. l i e r [10]. The directional correlation coefficients of the 702-405 keV cascade have been measured both with 211pb and 223Ra sources. The measurements were made in the actual geometry used for the magnetic moment determination. The data were analysed only for A 2 since the value of A 4 was found to be negligible [8, 7]. The directional correlation coefficient, A2, corrected for geometry, is in excellent agreement with e a r l i e r measurements [6, 7]. The magnetic moment measurements were made by an integral method using an external magnetic f i e l d of 18.3 kG applied perpendicular to the plane of the two gamma rays. The chance coincidence rate for any source was never more than 15~ of the total coincidence rate. The experimental a s y m m e t r y R(135 °) defined by
R(135o) = 2 W(135o, +H) - W(135o, -H) W(135 °, +H) + W(135 °, - H ) was measured with beth kinds of sources and the results are summarized in table 1, The measured a s y m m e t r y R is related to the L a r m o r precession frequency by
o~(=gl~NH/h~
R(135 °) = 3A2w~/(1 + 0.25A2)
,
where r i s the m e a n Hie of the 405 keV state. The m e a s u r e m e n t s with both kinds of s o u r c e s a g r e e d with each other, and the weighted a v e r a g e s of A 2
15 December 1965
Table 1 S,rmr~ary of the results. The directional correlation measurements on the 702 -405 keV cascade were analyzed only for ,42. The values of A 2 given in the table are not corrected for geometry. Source
.42
R(in %)
211pb 223Ra
-0.092 ± 0.007 -0.087 * 0.007
-1.39 :L0.40 -1.39 ± 0.21
Average
-0.090 ±0.005
-1.39 +0.19
g
1.27 -0.20
and R lead to a value of g = 1.27 * 0.20 c o r r e sponding to /~ = 4.45 ~- 0.70 n.m. We u s e d liquid s o u r c e s for the m e a s u r e m e n t s and no e x t r a nuc l e a r p e r t u r b a t i o n s on A2 w e r e a s s u m e d . The Schmtdt value for the m a g n e t i c m o m e n t of an f~ p r o t o n i s 5.79 n . m . The m e a s u r e d value of /~ i s ' s u b s t a n t i a l l y lower, c o r r e s p o n d i n g to an effective spin g - f a c t o r g s eft = (0.52 ± 0.25)g s free" A s s u m i n g the 405 keV sta'te to be a pure f ! st~'te, 2 one could e s t i m a t e the effect of core p o l a r i z a t i o n in a m a n n e r s i m i l a r to that of the f i n e u t r o n - h o l e state in 207pb [4]. In this model, t~e m a g n e t i c m o m e n t o p e r a t o r i s modified to [2] t, op -- ~s.p. ÷ 8 g s S + g p ( - r 2 a h • The v a l u e s of 5g s and gD for the 208pb core have b e e n obtained [4] f r o m the m e a s u r e d m a g n e t i c m o m e n t s of the ground s t a t e s of 207pb and 209Bi as 5g s = 5.21 a n d g n = 3.10. A s s u m i n g tlmt the s a m e p a r a m e t e r s c~h~.racterize the 21Opb core also, one can c a l c u l a t e the m a g n e t i c m o m e n t of the f~ s t a t e in 21113i a s ~ = 3.59 n . m . which i s in f a i r a g r e e m e n t with the m e a s u r e d value of ~ = 4.45 ± 0.70 n.m. It would also be i n t e r e s t i n g to make a d e t a i l e d c a l c u l a t i o n on the l i n e s of ref. 3 for this case also. The f i r s t excited 2+ state i n 210pb i s at 780 keV. Hence one m a y also i n t e r p r e t the 405 keV state in 211Bi as a {(g~2)2+ , h i } l - state. In fact, the z e r o o r d e r energy2of such2a2state i s expected to be 780 keV while the e x c i t a t i o n e n e r g y of a pure f~2 s t a t e i s 910 keV in 209Bi. The l o w e r i n g of the e n e r g y of s u c h a ~- state to 405 keV m a y be due to n - p i n t e r a c t i o n s . The m a g n e t i c m o m e n t of such a c o n f i g u r a t i o n can be c a l c u l a t e d if the m a g n e t i c m o m e n t s of the h~ proton and the g ! n e u t r o n a r e known. Assum~ag/z = 4.08 n . m . 2 for the h i p r o t o n (from the m e a s u r e d value of 209Bi), and the Schmidt value for the g ! n e u t r o n , the expected m a g n e t i c m o m e n t of s u c h ~ configur a t i o n is 3.9 n . m . which i s also in good a g r e e m e n t with the e x p e r i m e n t a l value. A change i n the m a g n e t i c m o m e n t of a g l n e u t r o n away f r o m the Schmidt value would n o t ' a f f e c t the expected 579
Volume 19, number 7
PHYSICS LETTERS
value of the m a g n e t i c m o m e n t of a {(g92)~+, hA)_~" 2 ~ 2 state. In this context, it will be e x t r e m e l y i n f e r e s t i n g if the m a g n e t i c m o m e n t of the ground state of 21IBi could be m e a s u r e d . A c o m p a r i s o n of the g r o u n d - s t a t e m o m e n t s of 209Bi and 211Bi would then throw light on the effect of the two g9 n e u t r o n s in p o l a r i z i n g the core. Thus it is a p p a r e n t f r o m the above d i s c u s s i o n , that the m e a s u r e d m a g n e t i c m o m e n t of 405 keV (~-) state in 211Bi i n d i c a t e s p o s s i b l e core p o l a r i zation i r r e s p e c t i v e of whether the s t a t e i s a pure f~ state or a state f o r m e d by coupling the h9 p r o ° to the ( g ~2) 2 + state of the two n e u t r o n s . ton We wish to thank Drs. C. L. Rao and M. V. R a m a n a i h for t h e i r c o o p e r a t i o n in s e p a r a t i n g 223Ra f r o m 227Ac, Dr. K. S, Bhatki for his help in m i l k i n g 211pb s o u r c e s and Mr. H. C. J a i n for his help d u r i n g the c o u r s e of the m e a s u r e m e n t s .
15 December 1965
1. A.Bohr and B.R.Mottelscm, Lectures on nuclear structure and energy levels (Institute of Theoretical Physics and NORDITA, Copenhagen) 1962. 2. E. Bodenstedt and J. D. Rogers, in Perturbed angular correlations, eds.E.Karlsson, E.Matthias and K. Siegbahn (North-Holland Publ. Co., Amsterdam,
1964). 3. J.Blomqvist, N.Freed and H.O.Zetterstrb'm, Physics Letters 18 (1965) 47. 4. S.Gustsfsson, K.Johansson, E.Karlsson and A.G. Svensson, Physics Letters 10 (1964) 191. 5. A.Z.Hrynkiewicz, St.Szymczyk, T.Walczac, G. Zapalski, F. Baldeweg and G.Stiller, Physics Letters 6 (1963) 326. 6. S.E.Vandenbosch, C.V.K.Baba, P.R.Christensen, O. B.Nielsen and H.Nordby, Nuclear Phys.41 (1963) 482. 7. C.R.Cothern and R.D.Connor, Can.J. Phys.43 (1965) 383. 8. R.O.Mead and J.E.Draper, Phys. Rev. 139 (1965) B9. 9. E.K.Hyde, I.Perlman and G.T.Seaberg, in The nuclear properties of the heavy elements, Vol. II (Prentice-Hall, Inc., N.J.) 1964. 16. Y.K.Agarwal, C.V.K.Baba and S.K.Bhattacherjee, Nuclear Phys. 58 (1964) 651.
THE
IMPORTANCE OF THE STRONG ISOTOPIC SPIN DEPENDENCE OF PARTICLE-HOLE MATRIX ELEMENTS ON T H E M A N Y P A R T I C L E - M A N Y H O L E S T A T E S IN N U C L E I * L. ZAMICK P a l m e r P h y s i c a l L a b o r a t o r y , P r i n c e t o n University, P r i n c e t o n , N e w J e r s e y
Received 10 November 1965
Following the i d e a s of B a n s a l and F r e n c h [1, 2] v e r y closely, we s h a l l t r y to d e t e r m i n e some of the p r o p e r t i e s of the excited s t a t e s of n u c l e i whose c o n f i g u r a t i o n s c o n s i s t of holes in the l p s h e l l and p a r t i c l e s in the 2 s - l d shell. We s h a l l also c o n s i d e r the f ! s h e l l b r i e f l y . If we deal with ~nly p a r t i c l e s in a given s h e l l (no holes), we can expect c o n s i d e r a b l e s u c c e s s by a s s u m i n g that the p a r t i c l e - p a r t i c l e i n t e r a c t i o n is spin independent and isotopic s p i n independent. The s u p e r m u l t i p l e t theory and E l l i o t t ' s SU(3) s c h e m e a r e e x a m p l e s of this. It has been shown, however, by Bansal and F r e n c h [1, 2], that it is a g r a v e e r r o r to a s s u m e that the p a r t i c l e - h o l e i n t e r a c t i o n is independent of isotopic spin. If one e x a m i n e s the negative p a r i t y s t a t e s of 160, which a r e e i t h e r one p a r t i c l e - o n e hole or 3 - p a r t i c l e - 3 hole excitations, one s e e s i m m e d i a t e l y * This work was supported by the U. S. Atomic Energy Commission and the Higgins Scientific Trust Fund. 580
that the T = 1 s t a t e s lie c o n s i d e r a b l y higher in e n e r g y than the c o r r e s p o n d i n g T = O s t a t e s (about 5 MeV or more). If we make the somewhat crude a s s u m p t i o n , that the s p l i t t i n g of the T = 0 and T = 1 s t a t e s (the difference of t h e i r c e n t e r s of gravity) is much l a r g e r than the splitting of different s t a t e s with the s a m e isotopic spin, then we can, as the above a u t h o r s have done, a p p r o x i m a t e the p a r ticle hole i n t e r a c t i o n by a monopole potential Hmono = - a + bt 1 t 2 ,
(1)
where - a is the c e n t e r of g r a v i t y of all p a r t i c l e hole s t a t e s with a (2J+ 1)(2T+ 1) weighting, and b is the s e p a r a t i o n of the T = 1 and T = 0 cent e r s of gravity. We expect b to be l a r g e and positive. To the above we should add the Coulomb p a r t i c l e - h o l e energy, c, which acts between a proton and a proton hole. We shall take c to equal - 0.5 MeV. We now c o n s i d e r a n u c l e u s with rn holes in the